\chapter{Case Studies and Applications}
\label{chap:case_studies}

\section{Overview}

We present four case studies illustrating hierarchical cooperation at scale. Each aligns theoretical constructs with domain-specific constraints, drawing on metrics and protocols established earlier.

\section{Organizational Management}

A technology enterprise deploys a three-level governance structure (teams, departments, executive board). We model decision queues, communication policies, and governance escalations.

\begin{itemize}
    \item \textbf{Model}: Queueing network with priority classes (Chapter~\ref{chap:stochastic}) and option-based planning (Chapter~\ref{chap:math_framework}).
    \item \textbf{Metrics}: Transfer entropy between levels, service-level variance, compliance incidents.
    \item \textbf{Findings}: Controlled randomness in ideation phases improves innovation metrics without violating throughput constraints when governance thresholds are enforced.
\end{itemize}

\section{Traffic Coordination}

We examine adaptive traffic signal control using hierarchical reinforcement learning.

\begin{itemize}
    \item \textbf{Model}: Intersections (micro) coordinated by district controllers (meso) and central traffic management (macro).
    \item \textbf{Metrics}: Average delay, queue lengths, phase entropy, regret of adaptive controllers.
    \item \textbf{Insights}: Multi-level options accelerate convergence and handle demand surges, as predicted by \cref{thm:option_improvement}.
\end{itemize}

\section{Ecological Resource Management}

In ecological conservation, local ranger units, regional planners, and national policy interact.

\begin{itemize}
    \item \textbf{Model}: Agent-based simulation with resource stock dynamics, stochastic disturbances, and hierarchical governance.
    \item \textbf{Metrics}: Population stability, effective information between monitoring tiers, probability of policy violations.
    \item \textbf{Outcome}: Balanced noise scheduling (\cref{prop:useful_noise}) allows adaptive exploration while maintaining ecological thresholds.
\end{itemize}

\section{Social Information Dynamics}

We study online platforms where moderators and algorithms enforce rules.

\begin{itemize}
    \item \textbf{Model}: Opinion dynamics with hierarchical moderation, leveraging statistical mechanics analogues for polarization and consensus.
    \item \textbf{Metrics}: Entropy of opinion distribution, mutual information between moderation actions and community health signals, governance response time.
    \item \textbf{Lessons}: Phase-transition analysis (Chapter~\ref{chap:stat_mech}) identifies tipping points; early detection via information metrics enables timely interventions.
\end{itemize}

\section{Cross-Case Synthesis}

\begin{table}[H]
    \centering
    \caption{Cross-case alignment with theoretical constructs}
    \label{tab:case_alignment}
    \begin{tabular}{p{3.5cm}p{3.5cm}p{3.5cm}}
        \toprule
        Domain & Dominant mechanism & Key validation artifact \\
        \midrule
        Organizational management & Queue stability + governance monitors & Queueing metrics dashboard, governance audit logs \\
        Traffic coordination & Hierarchical POMDP with options & Simulation runs with regret analysis \\
        Ecological management & Noise shaping + information bottlenecks & Effective information traces, resilience indicators \\
        Social dynamics & Phase transitions + moderation thresholds & Mutual information alerts, phase diagrams \\
        \bottomrule
    \end{tabular}
\end{table}

Each case study links to reproducibility packages in `artifacts/` containing configuration files, notebooks, and summary reports.

